Subgroups — C₂×C₅×#4837 #14412997

Order 1920.

1152 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×ΓL(1,𝔽₂₅)	C₂	1	2	yes	maximal
2	C₂×C₄²×C₅×D₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×C₅×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×Dic₃⋊C₈	C₂	1	2	yes	maximal, complemented
5	C₂×C₅×C₄⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4837	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₅×#423	—	3	1	no	maximal, Hall
8	C₂²×C₄×C₅×D₃	C₄	1	1	yes	characteristic
9	C₂²×C₄×C₅×D₃	C₄	1	1	yes	characteristic
10	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
12	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₅×Dic₃	C₄	1	1	yes	characteristic
14	C₂×C₄×C₅×Dic₃	C₄	1	1	yes	characteristic
15	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
16	C₂²×C₅×C₃⋊C₈	C₂²	1	2	yes	—
17	C₂×C₅×ΓL(1,𝔽₂₅)	—	2	8	no	—
18	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	8	yes	—
19	C₄²×C₅×D₃	C₄	1	4	yes	—
20	C₄²×C₅×D₃	C₂²	1	4	yes	—
21	C₃×C₅×C₄⋊C₈	C₂²	1	4	yes	complemented
22	C₅×Dic₃⋊C₈	C₂²	1	8	yes	complemented
23	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	4	yes	complemented
24	C₂×#4837	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
25	C₂²×C₅×M₁₆	—	3	2	no	—
26	C₂²×C₄²×C₅	—	3	1	no	—
27	C₅×#423	—	3	8	no	—
28	C₂×C₅×C₄⋊C₈	—	3	2	no	—
29	C₂×C₅×C₄⋊C₈	—	3	1	no	—
30	C₂×C₅×C₄⋊C₈	D₃	1	1	yes	characteristic, complemented
31	C₂³×C₅×D₃	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
34	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
35	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
36	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
37	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
38	C₂×C₄×C₅×D₃	—	2	4	no	—
39	C₂×C₄×C₅×D₃	—	2	4	no	—
40	C₂×C₄×C₅×D₃	C₂×C₄	1	4	yes	—
41	C₂×C₄×C₅×D₃	C₂×C₄	1	4	yes	—
42	C₂×C₄×C₅×D₃	C₂×C₄	1	2	yes	—
43	C₂×C₄×C₅×D₃	D₄	1	4	yes	—
44	C₂×C₄×C₅×D₃	Q₈	1	4	yes	—
45	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
46	C₂×C₃×C₅×C₈	—	2	4	no	—
47	C₂×C₃×C₅×C₈	C₂³	1	4	yes	—
48	C₃×C₄²×C₅	C₂×C₄	1	2	yes	—
49	C₃×C₄²×C₅	C₂³	1	2	yes	—
50	C₄×C₅×Dic₃	C₂×C₄	1	2	yes	—
51	C₄×C₅×Dic₃	C₂×C₄	1	4	yes	—
52	C₄×C₅×Dic₃	C₂×C₄	1	4	yes	—
53	C₄×C₅×Dic₃	C₂³	1	2	yes	—
54	C₂×C₅×C₃⋊C₈	—	2	4	no	—
55	C₂×C₅×C₃⋊C₈	C₂³	1	4	yes	—
56	C₅×ΓL(1,𝔽₂₅)	—	2	16	no	—
57	C₂²×ΓL(1,𝔽₂₅)	C₂×C₅	1	2	yes	—
58	C₂×C₄²×D₃	C₂×C₅	1	1	yes	characteristic
59	C₂×C₃×C₄⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
60	C₂×Dic₃⋊C₈	C₂×C₅	1	2	yes	complemented
61	C₂×C₄⋊(C₃⋊C₈)	C₂×C₅	1	1	yes	characteristic, complemented
62	#4837	C₂×C₅	1	8	yes	direct product factor
63	C₂³×C₄×C₅	—	3	1	no	—
64	C₂³×C₄×C₅	—	3	1	no	—
65	C₂³×C₄×C₅	—	3	1	no	—
66	C₂×C₅×M₁₆	—	3	8	no	—
67	C₂×C₅×M₁₆	—	6	8	no	—
68	C₂²×C₅×C₈	—	3	2	no	—
69	C₂²×C₅×C₈	C₂×D₃	1	2	yes	—
70	C₂×C₄²×C₅	—	3	1	no	—
71	C₂×C₄²×C₅	—	3	1	no	—
72	C₂×C₄²×C₅	—	3	1	no	—
73	C₂×C₄²×C₅	—	3	4	no	—
74	C₂×C₄²×C₅	—	3	4	no	—
75	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
76	C₅×C₄⋊C₈	—	3	8	no	—
77	C₅×C₄⋊C₈	—	3	4	no	—
78	C₅×C₄⋊C₈	C₂×D₃	1	4	yes	complemented
79	C₂×#423	—	3	1	no	Sylow
80	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
81	C₂²×C₅×D₃	—	2	2	no	—
82	C₂²×C₅×D₃	—	2	2	no	—
83	C₂²×C₅×D₃	C₄⋊C₄	1	4	yes	—
84	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
85	C₂×C₃×C₄×C₅	—	2	2	no	—
86	C₂×C₃×C₄×C₅	M₁₆	1	4	yes	complemented
87	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
88	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
89	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
90	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
91	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
92	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
93	C₂×C₅×Dic₃	—	2	2	no	—
94	C₂×C₅×Dic₃	C₄⋊C₄	1	4	yes	—
95	C₂×C₅×Dic₃	M₁₆	1	4	yes	complemented
96	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
97	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
98	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
99	C₄×C₅×D₃	—	2	8	no	—
100	C₄×C₅×D₃	—	2	8	no	—
101	C₄×C₅×D₃	C₄⋊C₄	1	8	yes	—
102	C₄×C₅×D₃	C₂×D₄	1	4	yes	—
103	C₄×C₅×D₃	C₂×Q₈	1	4	yes	—
104	C₃×C₅×C₈	—	2	4	no	—
105	C₅×C₃⋊C₈	—	2	4	no	—
106	C₂²×C₄×D₃	C₄×C₅	1	1	yes	characteristic
107	C₂²×C₄×D₃	C₄×C₅	1	1	yes	characteristic
108	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
109	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	—
110	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
111	C₂×C₄×Dic₃	C₄×C₅	1	1	yes	characteristic
112	C₂×C₄×Dic₃	C₄×C₅	1	1	yes	characteristic
113	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
114	C₂²×C₃⋊C₈	C₂²×C₅	1	2	yes	—
115	C₂×ΓL(1,𝔽₂₅)	—	2	8	no	—
116	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	8	yes	—
117	C₄²×D₃	C₄×C₅	1	4	yes	—
118	C₄²×D₃	C₂²×C₅	1	4	yes	—
119	C₃×C₄⋊C₈	C₂²×C₅	1	4	yes	complemented
120	Dic₃⋊C₈	C₂²×C₅	1	8	yes	complemented
121	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	4	yes	complemented
122	C₂⁴×C₅	—	3	1	no	—
123	C₂²×C₄×C₅	—	3	1	no	—
124	C₂²×C₄×C₅	—	3	1	no	—
125	C₂²×C₄×C₅	—	3	2	no	—
126	C₂²×C₄×C₅	—	3	4	no	—
127	C₂²×C₄×C₅	—	3	4	no	—
128	C₂²×C₄×C₅	—	3	2	no	—
129	C₂²×C₄×C₅	—	3	1	no	—
130	C₂²×C₄×C₅	—	3	4	no	—
131	C₂²×C₄×C₅	—	3	4	no	—
132	C₂²×C₄×C₅	—	6	4	no	—
133	C₂²×C₄×C₅	—	6	4	no	—
134	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
135	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
136	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
137	C₅×M₁₆	—	6	16	no	—
138	C₂×C₅×C₈	—	2	4	no	—
139	C₂×C₅×C₈	—	3	4	no	—
140	C₂×C₅×C₈	—	6	4	no	—
141	C₂×C₅×C₈	C₂²×D₃	1	4	yes	—
142	C₄²×C₅	—	3	4	no	—
143	C₄²×C₅	—	3	4	no	—
144	C₄²×C₅	—	3	2	no	—
145	C₄²×C₅	—	3	2	no	—
146	C₄²×C₅	C₄×D₃	1	2	yes	—
147	C₄²×C₅	C₂²×D₃	1	2	yes	—
148	C₂²×M₁₆	—	3	2	no	—
149	C₂²×C₄²	—	3	1	no	—
150	#423	—	3	8	no	—
151	C₂×C₄⋊C₈	—	3	2	no	—
152	C₂×C₄⋊C₈	—	3	1	no	—
153	C₂×C₄⋊C₈	C₅×D₃	1	1	yes	characteristic, complemented
154	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	2	yes	—
155	C₂²×C₃×C₅	C₂×M₁₆	1	2	yes	—
156	C₂²×C₃×C₅	C₂×M₁₆	1	2	yes	—
157	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
158	C₂×C₅×D₃	—	2	2	no	—
159	C₂×C₅×D₃	—	2	2	no	—
160	C₂×C₅×D₃	—	2	8	no	—
161	C₂×C₅×D₃	C₂×C₄⋊C₄	1	4	yes	—
162	C₃×C₄×C₅	—	2	2	no	—
163	C₃×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
164	C₃×C₄×C₅	C₂×M₁₆	1	4	yes	complemented
165	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
166	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
167	C₅×Dic₃	—	2	2	no	—
168	C₅×Dic₃	C₂×C₄⋊C₄	1	4	yes	—
169	C₅×Dic₃	C₂×M₁₆	1	4	yes	complemented
170	C₂³×D₃	C₂×C₄×C₅	1	1	yes	characteristic
171	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
172	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
173	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
174	C₂²×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
175	C₂²×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
176	C₂²×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
177	C₂×C₄×D₃	—	2	4	no	—
178	C₂×C₄×D₃	—	2	4	no	—
179	C₂×C₄×D₃	C₂×C₄×C₅	1	4	yes	—
180	C₂×C₄×D₃	C₂×C₄×C₅	1	4	yes	—
181	C₂×C₄×D₃	C₂×C₄×C₅	1	2	yes	—
182	C₂×C₄×D₃	C₅×D₄	1	4	yes	—
183	C₂×C₄×D₃	C₅×Q₈	1	4	yes	—
184	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
185	C₂×C₃×C₈	—	2	4	no	—
186	C₂×C₃×C₈	C₂³×C₅	1	4	yes	—
187	C₃×C₄²	C₂×C₄×C₅	1	2	yes	—
188	C₃×C₄²	C₂³×C₅	1	2	yes	—
189	C₄×Dic₃	C₂×C₄×C₅	1	2	yes	—
190	C₄×Dic₃	C₂×C₄×C₅	1	4	yes	—
191	C₄×Dic₃	C₂×C₄×C₅	1	4	yes	—
192	C₄×Dic₃	C₂³×C₅	1	2	yes	—
193	C₂×C₃⋊C₈	—	2	4	no	—
194	C₂×C₃⋊C₈	C₂³×C₅	1	4	yes	—
195	ΓL(1,𝔽₂₅)	—	2	16	no	—
196	C₂³×C₅	—	3	4	no	—
197	C₂³×C₅	—	3	2	no	—
198	C₂³×C₅	—	6	2	no	—
199	C₂³×C₅	—	6	2	no	—
200	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
201	C₂×C₄×C₅	—	2	2	no	—
202	C₂×C₄×C₅	—	3	4	no	—
203	C₂×C₄×C₅	—	3	4	no	—
204	C₂×C₄×C₅	—	3	2	no	—
205	C₂×C₄×C₅	—	3	2	no	—
206	C₂×C₄×C₅	—	3	8	no	—
207	C₂×C₄×C₅	—	3	4	no	—
208	C₂×C₄×C₅	—	3	4	no	—
209	C₂×C₄×C₅	—	3	2	no	—
210	C₂×C₄×C₅	—	6	8	no	—
211	C₂×C₄×C₅	—	6	2	no	—
212	C₂×C₄×C₅	—	6	8	no	—
213	C₂×C₄×C₅	ΓL(1,𝔽₂₅)	1	4	yes	complemented
214	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
215	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
216	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
217	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
218	C₂×C₄×C₅	D₃×Q₈	1	2	yes	—
219	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
220	C₅×C₈	—	2	4	no	—
221	C₅×C₈	—	6	4	no	—
222	C₂³×C₄	—	3	1	no	—
223	C₂³×C₄	—	3	1	no	—
224	C₂³×C₄	—	3	1	no	—
225	C₂×M₁₆	—	3	8	no	—
226	C₂×M₁₆	—	6	8	no	—
227	C₂²×C₈	—	3	2	no	—
228	C₂²×C₈	C₂×C₅×D₃	1	2	yes	—
229	C₂×C₄²	—	3	1	no	—
230	C₂×C₄²	—	3	1	no	—
231	C₂×C₄²	—	3	1	no	—
232	C₂×C₄²	—	3	4	no	—
233	C₂×C₄²	—	3	4	no	—
234	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
235	C₄⋊C₈	—	3	8	no	—
236	C₄⋊C₈	—	3	4	no	—
237	C₄⋊C₈	C₂×C₅×D₃	1	4	yes	complemented
238	C₂×C₃×C₅	#423	1	4	yes	complemented
239	C₂×C₃×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
240	C₂×C₃×C₅	C₂²×M₁₆	1	1	yes	characteristic
241	C₂×C₃×C₅	C₂²×M₁₆	1	1	yes	characteristic
242	C₅×D₃	—	2	4	no	—
243	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
244	C₂²×D₃	—	2	2	no	—
245	C₂²×D₃	—	2	2	no	—
246	C₂²×D₃	C₅×C₄⋊C₄	1	4	yes	—
247	C₂²×D₃	C₂²×C₄×C₅	1	2	yes	—
248	C₂×C₃×C₄	—	2	2	no	—
249	C₂×C₃×C₄	C₅×M₁₆	1	4	yes	complemented
250	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
251	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
252	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
253	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
254	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
255	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
256	C₂×Dic₃	—	2	2	no	—
257	C₂×Dic₃	C₅×C₄⋊C₄	1	4	yes	—
258	C₂×Dic₃	C₅×M₁₆	1	4	yes	complemented
259	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
260	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
261	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
262	C₄×D₃	—	2	8	no	—
263	C₄×D₃	—	2	8	no	—
264	C₄×D₃	C₅×C₄⋊C₄	1	8	yes	—
265	C₄×D₃	C₂×C₅×D₄	1	4	yes	—
266	C₄×D₃	C₂×C₅×Q₈	1	4	yes	—
267	C₃×C₈	—	2	4	no	—
268	C₃⋊C₈	—	2	4	no	—
269	C₂²×C₅	—	3	4	no	—
270	C₂²×C₅	—	6	2	no	—
271	C₂²×C₅	—	6	2	no	—
272	C₂²×C₅	—	6	8	no	—
273	C₂²×C₅	D₃×C₄⋊C₄	1	2	yes	—
274	C₂²×C₅	C₂×ΓL(1,𝔽₂₅)	1	2	yes	—
275	C₂²×C₅	D₃×M₁₆	1	2	yes	—
276	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
277	C₄×C₅	—	2	2	no	—
278	C₄×C₅	—	3	4	no	—
279	C₄×C₅	—	3	4	no	—
280	C₄×C₅	—	6	2	no	—
281	C₄×C₅	D₃×C₄⋊C₄	1	2	yes	—
282	C₄×C₅	C₂×ΓL(1,𝔽₂₅)	1	4	yes	complemented
283	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
284	C₄×C₅	C₂×D₃×Q₈	1	1	yes	characteristic
285	C₂⁴	—	3	1	no	—
286	C₂²×C₄	—	3	1	no	—
287	C₂²×C₄	—	3	1	no	—
288	C₂²×C₄	—	3	2	no	—
289	C₂²×C₄	—	3	4	no	—
290	C₂²×C₄	—	3	4	no	—
291	C₂²×C₄	—	3	2	no	—
292	C₂²×C₄	—	3	1	no	—
293	C₂²×C₄	—	3	4	no	—
294	C₂²×C₄	—	3	4	no	—
295	C₂²×C₄	—	6	4	no	—
296	C₂²×C₄	—	6	4	no	—
297	C₂²×C₄	C₄×C₅×D₃	1	1	yes	characteristic
298	C₂²×C₄	C₄×C₅×D₃	1	1	yes	characteristic
299	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
300	M₁₆	—	6	16	no	—
301	C₂×C₈	—	2	4	no	—
302	C₂×C₈	—	3	4	no	—
303	C₂×C₈	—	6	4	no	—
304	C₂×C₈	C₂²×C₅×D₃	1	4	yes	—
305	C₄²	—	3	4	no	—
306	C₄²	—	3	4	no	—
307	C₄²	—	3	2	no	—
308	C₄²	—	3	2	no	—
309	C₄²	C₄×C₅×D₃	1	2	yes	—
310	C₄²	C₂²×C₅×D₃	1	2	yes	—
311	C₃×C₅	C₂×#423	1	1	yes	characteristic, complemented, Hall
312	C₂²×C₃	C₂×C₅×C₄⋊C₄	1	2	yes	—
313	C₂²×C₃	C₂×C₅×M₁₆	1	2	yes	—
314	C₂²×C₃	C₂×C₅×M₁₆	1	2	yes	—
315	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
316	C₂×D₃	—	2	8	no	—
317	C₂×D₃	—	2	2	no	—
318	C₂×D₃	—	2	2	no	—
319	C₂×D₃	C₂×C₅×C₄⋊C₄	1	4	yes	—
320	C₃×C₄	—	2	2	no	—
321	C₃×C₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
322	C₃×C₄	C₂×C₅×M₁₆	1	4	yes	complemented
323	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
324	C₃×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
325	Dic₃	—	2	2	no	—
326	Dic₃	C₂×C₅×C₄⋊C₄	1	4	yes	—
327	Dic₃	C₂×C₅×M₁₆	1	4	yes	complemented
328	C₂×C₅	—	6	4	no	—
329	C₂×C₅	#4837	1	4	yes	direct product factor
330	C₂×C₅	C₂×D₃×C₄⋊C₄	1	1	yes	characteristic
331	C₂×C₅	C₂²×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
332	C₂×C₅	C₂×D₃×M₁₆	1	1	yes	characteristic
333	C₂³	—	3	4	no	—
334	C₂³	—	3	2	no	—
335	C₂³	—	6	2	no	—
336	C₂³	—	6	2	no	—
337	C₂³	C₂×C₄×C₅×D₃	1	1	yes	characteristic
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	3	4	no	—
340	C₂×C₄	—	3	4	no	—
341	C₂×C₄	—	3	2	no	—
342	C₂×C₄	—	3	2	no	—
343	C₂×C₄	—	3	8	no	—
344	C₂×C₄	—	3	4	no	—
345	C₂×C₄	—	3	4	no	—
346	C₂×C₄	—	3	2	no	—
347	C₂×C₄	—	6	8	no	—
348	C₂×C₄	—	6	2	no	—
349	C₂×C₄	—	6	8	no	—
350	C₂×C₄	C₅×ΓL(1,𝔽₂₅)	1	4	yes	complemented
351	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
352	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
353	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
354	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
355	C₂×C₄	C₅×D₃×Q₈	1	2	yes	—
356	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
357	C₈	—	2	4	no	—
358	C₈	—	6	4	no	—
359	C₂×C₃	C₅×#423	1	4	yes	complemented
360	C₂×C₃	C₂²×C₅×C₄⋊C₄	1	1	yes	characteristic
361	C₂×C₃	C₂²×C₅×M₁₆	1	1	yes	characteristic
362	C₂×C₃	C₂²×C₅×M₁₆	1	1	yes	characteristic
363	D₃	—	2	4	no	—
364	C₅	C₂×#4837	1	1	yes	characteristic, direct product factor, Sylow
365	C₂²	—	3	4	no	—
366	C₂²	—	6	2	no	—
367	C₂²	—	6	2	no	—
368	C₂²	—	6	8	no	—
369	C₂²	C₅×D₃×C₄⋊C₄	1	2	yes	—
370	C₂²	C₂×C₅×ΓL(1,𝔽₂₅)	1	2	yes	—
371	C₂²	C₅×D₃×M₁₆	1	2	yes	—
372	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
373	C₄	—	2	2	no	—
374	C₄	—	3	4	no	—
375	C₄	—	3	4	no	—
376	C₄	—	6	2	no	—
377	C₄	C₅×D₃×C₄⋊C₄	1	2	yes	—
378	C₄	C₂×C₅×ΓL(1,𝔽₂₅)	1	4	yes	complemented
379	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
380	C₄	C₂×C₅×D₃×Q₈	1	1	yes	characteristic
381	C₃	C₂×C₅×#423	1	1	yes	characteristic, complemented, Sylow
382	C₂	—	6	4	no	—
383	C₂	C₅×#4837	1	4	yes	direct product factor
384	C₂	C₂×C₅×D₃×C₄⋊C₄	1	1	yes	characteristic
385	C₂	C₂²×C₅×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
386	C₂	C₂×C₅×D₃×M₁₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₅	C₂²×D₃
commutator	C₂²×C₃	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₂×C₃×C₅×C₄⋊C₈	C₂
socle	C₂³×C₃×C₅	C₂²×C₄
prime radical	C₂³×C₅×D₃	C₂×C₄
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₂×C₅×C₄⋊C₈	D₃
hypocenter	C₃	C₂×C₅×#423
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ C₂×C₅×C₄⋊C₈

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
3. C₂×C₃×C₅×C₄⋊C₈	C₂	semidirect
4. C₂×C₅×Dic₃⋊C₈	C₂	semidirect
5. C₂×C₅×C₄⋊(C₃⋊C₈)	C₂	semidirect
6. C₅×#4837	C₂	direct (N × H)
21. C₃×C₅×C₄⋊C₈	C₂²	semidirect
22. C₅×Dic₃⋊C₈	C₂²	semidirect
23. C₅×C₄⋊(C₃⋊C₈)	C₂²	semidirect
24. C₂×#4837	C₅	direct (N × H)
30. C₂×C₅×C₄⋊C₈	D₃	semidirect
59. C₂×C₃×C₄⋊C₈	C₂×C₅	semidirect
60. C₂×Dic₃⋊C₈	C₂×C₅	semidirect
61. C₂×C₄⋊(C₃⋊C₈)	C₂×C₅	semidirect
62. #4837	C₂×C₅	direct (N × H)
78. C₅×C₄⋊C₈	C₂×D₃	semidirect
86. C₂×C₃×C₄×C₅	M₁₆	semidirect
95. C₂×C₅×Dic₃	M₁₆	semidirect
119. C₃×C₄⋊C₈	C₂²×C₅	semidirect
120. Dic₃⋊C₈	C₂²×C₅	semidirect
121. C₄⋊(C₃⋊C₈)	C₂²×C₅	semidirect
153. C₂×C₄⋊C₈	C₅×D₃	semidirect
164. C₃×C₄×C₅	C₂×M₁₆	semidirect
169. C₅×Dic₃	C₂×M₁₆	semidirect
213. C₂×C₄×C₅	ΓL(1,𝔽₂₅)	semidirect
237. C₄⋊C₈	C₂×C₅×D₃	semidirect
238. C₂×C₃×C₅	#423	semidirect
249. C₂×C₃×C₄	C₅×M₁₆	semidirect
258. C₂×Dic₃	C₅×M₁₆	semidirect
282. C₄×C₅	C₂×ΓL(1,𝔽₂₅)	semidirect
311. C₃×C₅	C₂×#423	semidirect
322. C₃×C₄	C₂×C₅×M₁₆	semidirect
327. Dic₃	C₂×C₅×M₁₆	semidirect
329. C₂×C₅	#4837	direct (N × H)
350. C₂×C₄	C₅×ΓL(1,𝔽₂₅)	semidirect
359. C₂×C₃	C₅×#423	semidirect
364. C₅	C₂×#4837	direct (N × H)
378. C₄	C₂×C₅×ΓL(1,𝔽₂₅)	semidirect
381. C₃	C₂×C₅×#423	semidirect
383. C₂	C₅×#4837	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₅×ΓL(1,𝔽₂₅)	2
C₂×C₄²×C₅×D₃	2
C₂×C₃×C₅×C₄⋊C₈	2
C₂×C₅×Dic₃⋊C₈	2
C₂×C₅×C₄⋊(C₃⋊C₈)	2
C₅×#4837	2
C₂×C₅×#423	3
C₂×#4837	5

Subgroups — C2×C5×#4837 #14412997

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#4837 #14412997